Greece is a good budget option. But consider going for a week at least.
Apart from that, Serbia, Romania and Bulgaria are beautiful destinations that are also some of the cheapest in Europe.
I HAVE BEEN TO PRAGUE AND AUSTRIA. Both are quite budget places to visit. If you are going solo or with friends, then you can always go for hostels. However, plan your visit atleast for 8-10 days. My trip duration was 20 days and even that was not enough/
Hey Tanupriya, Europe in October is a good decision. Tripoto has some interesting packages for Europe. Please take a look, fill the form and someone will get in touch with you.